Showing papers in "Physical Review B in 2019"
TL;DR: In this paper, the authors derive a geometrical approach for the exact determination of the skin-mode spectrum of non-Hermitian particle-hole symmetric Hamiltonians based on complex analysis.
Abstract: Non-Hermitian systems can exhibit a counterintuitive phenomenon where a single local boundary or disorder modifies the entire spectrum, no matter how large the system is. In such cases, all bulk modes become localized ``skin'' modes, and usual bulk topological invariants no longer correctly predict topological boundary modes. Generalizing Laughlin's gauge argument to complex fluxes, the authors derive a geometrical approach for the exact determination of the skin-mode spectrum. They also devise a new topological criterion for non-Hermitian particle-hole symmetric Hamiltonians based on complex analysis.
567 citations
TL;DR: In this paper, the authors systematically studied charge fractionalization in higher-order topological insulators and showed that charge can be fractionally quantized in units of $e/n.
Abstract: Building upon the concepts of band representations and their relation to localized Wannier functions, the authors systematically study charge fractionalization in higher-order topological insulators. They show that, when protected by ${C}_{n}$ rotation symmetries, charge can be fractionally quantized in units of $e/n$. The authors build topological indices for ${C}_{n}$-symmetric higher-order topological insulators in class AI. Due to an algebraic structure of the topological classification of these phases, these indices apply even to fragile phases, which lack a Wannier description, but for which a ``generalized'' Wannier description can be formulated.
401 citations
TL;DR: In this article, the authors report on the construction of a faithful tight-binding model for twisted bilayer graphene, which led them to a precise characterization of its band topology.
Abstract: The authors report on the construction of a faithful tight-binding model for twisted bilayer graphene, which led them to a precise characterization of its band topology.
325 citations
TL;DR: In this article, a toy model of Bell pair dynamics was constructed and it was shown that measurements can keep a system in a state of low, i.e., area-law, entanglement, in contrast with the volume-law entenglement produced by generic pure unitary time evolution.
Abstract: Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low, i.e., area-law, entanglement, in contrast with the volume-law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area-law entanglement for any measurement rate, as seen in certain noninteracting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law, and critical ``fixed points.'' We also discuss a Floquet random unitary circuit, where the answers depend on the order of limits---one order of limits yields area-law entanglement for any nonzero measurement rate, whereas a different order of limits allows for an arealaw--volumelaw transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume-law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase.
313 citations
TL;DR: The role of non-Hermitian AB and chiral inversion symmetry for the breakdown and recovery of the bulk-boundary correspondence was investigated in this paper, where the average value of Pauli matrices under the eigenstate of chiral-inversion-symmetric Bloch Hamiltonian defines a vector field; the vorticity of topological defects in the vector field is a topological invariant.
Abstract: Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of the Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiral-inversion-symmetric Bloch Hamiltonian defines a vector field; the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by the non-Hermitian AB effect and chiral inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding the non-Hermitian topological phases of matter.
307 citations
TL;DR: In this paper, it was shown that in many graphene moir\'e structures not only are the electronic bands narrow enough for Coulomb interaction to be important, but they are also topologically nontrivial.
Abstract: The competition between the kinetic energy of electrons in a crystal and the inter-electron Coulomb repulsion underlies many fascinating phenomena in quantum materials. Superlattices formed from moir\'e patterns in graphene structures have emerged as tunable platforms for such physics. This paper shows that in many graphene moir\'e structures not only are the electronic bands narrow enough for Coulomb interaction to be important, but they are also topologically nontrivial. This setting of a strong correlated partially filled topological band promises to lead to many novel phenomena.
304 citations
TL;DR: In this article, the atomic cluster expansion is developed as a complete descriptor of the local atomic environment, including multicomponent materials, and its relation to a number of other descriptors and potentials is discussed.
Abstract: The atomic cluster expansion is developed as a complete descriptor of the local atomic environment, including multicomponent materials, and its relation to a number of other descriptors and potentials is discussed. The effort for evaluating the atomic cluster expansion is shown to scale linearly with the number of neighbors, irrespective of the order of the expansion. Application to small Cu clusters demonstrates smooth convergence of the atomic cluster expansion to meV accuracy. By introducing nonlinear functions of the atomic cluster expansion an interatomic potential is obtained that is comparable in accuracy to state-of-the-art machine learning potentials. Because of the efficient convergence of the atomic cluster expansion relevant subspaces can be sampled uniformly and exhaustively. This is demonstrated by testing against a large database of density functional theory calculations for copper.
297 citations
TL;DR: In this paper, the authors derive a comprehensive 38-fold topological classification of non-Hermitian systems with generic non-hermitian symmetry classes and provide a framework for the experimental design and engineering of symmetry-protected topological systems.
Abstract: Classifications of symmetry-protected topological phases provide a framework to understand systematically the physical properties and potential applications of topological systems. Here, the authors derive a comprehensive 38-fold topological classification of non-Hermitian systems with generic non-Hermitian symmetry classes. Two independent generalizations of Kramers' degeneracy to the non-Hermitian setting are presented. The nature of the non-Hermitian topological invariants obtained in this classification is explained through worked-out examples, thus providing a framework for the experimental design and engineering of non-Hermitian symmetry-protected topological systems.
297 citations
TL;DR: In this article, the authors proposed a mechanism for interlayer magnetic interactions in a CrI${}_{3}$ bilayer based on the concept of covalent-like quasibonding, which offers significant alteration of interlayer wave function hybridization but small energetic difference between different stacking configurations.
Abstract: Interlayer magnetic interactions between two-dimension van der Waals layers are often thought to be weak or even negligible and their mechanism is largely unexplored. Here, the authors propose a mechanism for these interactions in a CrI${}_{3}$ bilayer, based on the concept of covalent-like quasibonding, which offers significant alteration of interlayer wave-function hybridization but small energetic difference between different stacking configurations. While a near-collinear coupling between two parallel spin-polarized I 5$p$ orbitals prefers interlayer ferromagnetism, a noncollinear one favors antiferromagnetism, which is tunable by surmounting a tiny energy barrier between two stacking orders. This explains experimental observations and suggests a strategy for designing interlayer magnetism.
276 citations
TL;DR: In this article, a comprehensive theory of symmetry fractionalization together with the properties of symmetry defects in topologically ordered phases of matter in two spatial dimensions was developed, and the full set of data, consistency conditions, and equivalences for a mathematical theory, known as a G-crossed braided tensor category, was introduced.
Abstract: This paper develops a comprehensive theory of symmetry fractionalization together with the properties of symmetry defects in topologically ordered phases of matter in two spatial dimensions. To do this, the authors also introduce the full set of data, consistency conditions, and equivalences for a mathematical theory, known as a G-crossed braided tensor category, that characterizes the algebraic braiding and fusion properties of symmetry defects. This theoretical framework can completely characterize and classify symmetry-enriched topological phases of matter in the presence of arbitrarily strong interactions in quantum many-body systems in two spatial dimensions.
266 citations
TL;DR: In this paper, the authors address the question of whether entanglement can sustain repeated measurements in a toy hybrid-circuit model, where qubits undergo both unitary time evolution and sporadic local measurements.
Abstract: Quantum information tends to spread out in interacting systems, leading to thermalization as characterized by the volume-law entropy of entanglement, while local measurements that extract classical information of the state tend to interrupt the propagation of information and reduce the entanglement entropy. Can entanglement sustain repeated measurements? The authors address this question in a toy hybrid-circuit model, where qubits undergo both unitary time evolution and sporadic local measurements. The phase diagram features a stable volume-law phase of entanglement for weak measurements and an area-law phase for strong measurements. The two domains in the diagram are separated by a single second-order phase transition. Characterization of both phases as well as of the critical point are presented.
TL;DR: A methodology based on the evolutionary algorithm USPEX and the machine-learning interatomic potentials actively learning on-the-fly allows for an automated construction of an interatomic interaction model from scratch, replacing the expensive density functional theory (DFT) and giving a speedup of several orders of magnitude.
Abstract: We propose a methodology for crystal structure prediction that is based on the evolutionary algorithm USPEX and the machine-learning interatomic potentials actively learning on-the-fly. Our methodology allows for an automated construction of an interatomic interaction model from scratch, replacing the expensive density functional theory (DFT) and giving a speedup of several orders of magnitude. Predicted low-energy structures are then tested on DFT, ensuring that our machine-learning model does not introduce any prediction error. We tested our methodology on prediction of crystal structures of carbon, high-pressure phases of sodium, and boron allotropes, including those that have more than 100 atoms in the primitive cell. All the the main allotropes have been reproduced, and a hitherto unknown 54-atom structure of boron has been predicted with very modest computational effort.
TL;DR: In this paper, the existence of symmetry-protected exceptional rings (SPERs) in non-Hermitian systems has been studied in the context of a correlated honeycomb lattice model whose single-particle spectrum is described by a nonhermitian Dirac Hamiltonian.
Abstract: Emergence of exceptional points in two dimensions is one of the remarkable phenomena in non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian physics. Specifically, we analyze chiral symmetric correlated systems in equilibrium where the non-Hermitian phenomena are induced by the finite lifetime of quasiparticles. Intriguingly, our analysis reveals that the combination of symmetry and non-Hermiticity results in topological degeneracies of energy bands which we call symmetry-protected exceptional rings (SPERs). We observe the emergence of SPERs by analyzing a non-Hermitian Dirac Hamiltonian. Furthermore, by employing the dynamical mean-field theory, we demonstrate the emergence of SPERs in a correlated honeycomb lattice model whose single-particle spectrum is described by a non-Hermitian Dirac Hamiltonian. We uncover that the SPERs survive even beyond the non-Hermitian Dirac Hamiltonian, which is related to a zeroth Chern number. The argument of symmetry protection also holds for three dimensions, elucidating the presence of a symmetry-protected exceptional torus.
TL;DR: In this paper, the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudomagnetic fields generated by the moir\'e pattern.
Abstract: We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudomagnetic fields generated by the moir\'e pattern. The two low-energy flat bands from each monolayer valley originate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $\ifmmode\pm\else\textpm\fi{}1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interactions would split the eightfold degeneracy (including valley and physical spin) of these zeroth pseudo Landau levels, and may lead to insulating phases with nonvanishing Chern numbers at integer fillings. Besides, we show that all the high-energy bands below or above the flat bands are also topologically nontrivial in the sense that for each valley the sum of their Berry phases is quantized as $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$. Such quantized Berry phases give rise to nearly flat edge states, which are dependent on truncations on the moir\'e length scale. Our paper provides a complete and clear picture for the electronic structure and topological properties of TBG, and has significant implications on the nature of the correlated insulating phase observed in experiments.
TL;DR: In this article, a generalized biorthogonal bulk-boundary correspondence is formulated for non-Hermitian Hamiltonians and higher-order topological phases, where the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems.
Abstract: Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface, and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.
TL;DR: In this article, the authors present a general and directly implementable tool to diagnose the full topological characterization of bands using Wilson flows, and find a general relation and unambiguous representation of these novel topological concepts.
Abstract: Recently, there has been rapid progress in classifying topological band structures by examining possible configurations, arising through consideration of the constraints of the underlying lattice symmetry. Apart from topologically stable and trivial bands, these pursuits have identified fragile topologies that can be trivialized by additional bands. The authors present a general and directly implementable tool to diagnose the full topological characterization of bands using Wilson flows. As a result, they find a general relation and unambiguous representation of these novel topological concepts.
TL;DR: In this article, an on-the-fly force field generation method is developed and applied to liquid-solid phase transitions, which allows the machine to automatically self-learn interatomic potentials during molecular dynamics simulations and to generate force fields with the distinctive chemical precision of first-principles methods.
Abstract: An on-the-fly force field generation method is developed and applied to liquid-solid phase transitions. The method allows the machine to automatically self-learn interatomic potentials during molecular dynamics simulations and to generate force fields with the distinctive chemical precision of first-principles methods. Applications show that more than 99% of the expensive first-principles calculations are bypassed, and molecular dynamics simulations are accelerated by more than two orders of magnitude already during learning, with many more orders during production runs.
TL;DR: In this paper, it was shown that topologically nontrivial band degeneracies can appear as exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries.
Abstract: Non-Hermiticity makes possible novel topological phenomena, which are notallowed in Hermitian systems. The authors show that topologically nontrivial band degeneracies can appear as exceptional surfaces in non-Hermitian systems with parity--time and parity--particle-hole symmetries. It is shown that when parity--time or parity--particle-hole symmetry is present, $d$-dimensional non-Hermitian systems can have $(d\ensuremath{-}1)$-dimensional exceptional surfaces. This work suggests new topological phases with nodal band structures protected by non-Hermitian topology and symmetry.
TL;DR: In this article, a rescaled transition point is proved for the non-Hermitian skin effect in a non-reciprocal quasiperiodic lattice and the Anderson localization is studied.
Abstract: Non-Hermiticity from nonreciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization (AL) in a nonreciprocal quasiperiodic lattice, dubbed nonreciprocal Aubry-Andr\'e model, and a rescaled transition point is exactly proved. The nonreciprocity can induce not only NHSEs but also the asymmetry in localized states, characterized by two Lyapunov exponents. Meanwhile, this transition is also topological, in the sense of a winding number associated with complex eigenenergies under periodic boundary conditions (PBCs), establishing a bulk-bulk correspondence. This interplay can be realized straightforwardly by an electrical circuit with only linear passive RLC components instead of elusive nonreciprocal ones, showing the transport of a continuous wave undergoes a transition between insulating and amplifying. This paradigmatic scheme can be immediately accessed in experiments even for more nonreciprocal models and will definitely inspire the study of interplay of NHSEs and ALs as well as more other quantum/topological phenomena in various systems.
TL;DR: In this article, an effective low-energy Hamiltonian for the parent compound NdNiO${}_{2}$, which is found to be strongly correlated with superconductivity, was constructed and a route for the design of novel nickelates where self-doping is suppressed.
Abstract: Motivated by the discovery of the nickelate superconductor Nd${}_{0.8}$Sr${}_{0.2}$NiO${}_{2}$, the authors construct an effective low-energy Hamiltonian for the parent compound NdNiO${}_{2}$, which is found to be strongly correlated. While high-T${}_{c}$ superconductivity emerges near the Mott-insulating phase in the cuprates, NdNiO${}_{2}$ is not a Mott insulator, because the 3$d$ ${x}^{2}$-${y}^{2}$ band of nickel is self-doped. The authors propose a route for the design of novel nickelates where self-doping is suppressed. If synthesized, such nickelates would provide a playground for the exploration of high-T${}_{c}$ superconductivity.
TL;DR: The notion of symmetry-protected non-Hermitian nodal phases was introduced in this paper, where the authors analyzed the importance of symmetry to the dissipative counterparts of topological semimetals in non-hermitian systems.
Abstract: Symmetry plays a paramount role for the classification of phases of matter occurring in nature. Combining symmetry analysis with concepts from topology that allow us to identify global and robust physical properties, new phases of quantum matter, such as topological insulators and semimetals, have been discovered in recent years. Here, the authors analyze in general and exemplify the importance of symmetries to the dissipative counterparts of topological semimetals in non-Hermitian systems, thus introducing the notion of symmetry-protected non-Hermitian nodal phases.
TL;DR: In this article, a general principle for constructing higher-order topological (HOT) phases was proposed, and it was shown that if a D-dimensional first-order or regular topological phase involves m Hermitian matrices that a...
Abstract: We propose a general principle for constructing higher-order topological (HOT) phases. We argue that if a D-dimensional first-order or regular topological phase involves m Hermitian matrices that a ...
TL;DR: In this paper, it was shown that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with small entropy, but only if the measurement strength exceeds a critical value.
Abstract: We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small entropy, but only if the measurement strength exceeds a critical value. We demonstrate this effect for a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. As opposed to projective measurements describing a restricted class of open systems, the measuring device is modeled as a continuous Gaussian probe, capturing a large class of environments. By employing data collapse and studying the enhanced fluctuations at the transition, we obtain a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. These findings provide guidance for quantum engineering of many-body systems by controlling their environment.
TL;DR: In this article, a higher-order topological insulator is realized in a circuit model and the authors demonstrate dynamical switching between topological and trivial phases as well as controllable interactions between topologically protected states.
Abstract: Higher-order topological insulators belong to a recently discovered class of materials where nontrivial topology results in boundary states with a dimensionality two or more below that of the bulk. This work realizes a higher-order topological insulator in a circuit model. By using nonlinear elements, the authors demonstrate dynamical switching between topological and trivial phases as well as controllable interactions between topologically protected states. The topological nature of the model is exhibited by direct extraction of the invariants from the measured boundary Green's functions.
TL;DR: In this paper, the experimental Hamiltonian exhibits nonthermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points.
Abstract: A recent experiment on a 51-atom Rydberg-blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this Rapid Communication, we show that the experimental Hamiltonian exhibits nonthermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.
TL;DR: In this article, the effect of electron-acoustic phonon interactions in twisted bilayer graphene on resistivity and superconductivity in the low-temperature phase diagram was studied.
Abstract: We study the effect of electron-acoustic phonon interactions in twisted bilayer graphene on resistivity in the high-temperature transport and superconductivity in the low-temperature phase diagram. We theoretically show that twisted bilayer graphene should have an enhanced and strongly twist-angle dependent linear-in-temperature resistivity in the metallic regime with the resistivity magnitude increasing as the twist angle approaches the magic angle. The slope of the resistivity versus temperature could approach one hundred ohm per kelvin with a strong angle dependence, but with a rather weak dependence on the carrier density. This higher-temperature density-independent linear-in-$T$ resistivity crosses over to a ${T}^{4}$ dependence at a low density-dependent characteristic temperature, becoming unimportant at low temperatures. This angle-tuned resistivity enhancement arises from the huge increase in the effective electron-acoustic phonon coupling in the system due to the suppression of graphene Fermi velocity induced by the flat-band condition in the moir\'e superlattice system. Our calculated temperature dependence is reminiscent of the so-called ``strange metal'' transport behavior except that it is arising from the ordinary electron-phonon coupling in a rather unusual parameter space due to the generic moir\'e flat-band structure of twisted bilayer graphene. We also show that the same enhanced electron-acoustic phonon coupling also mediates effective attractive interactions in $s,\phantom{\rule{4pt}{0ex}}p,\phantom{\rule{4pt}{0ex}}d$, and $f$ pairing channels with a theoretical superconducting transition temperature on the order of $\ensuremath{\sim}5$ K near magic angle. The fact that ordinary acoustic phonons can produce exotic non-$s$-wave superconducting pairing arises from the unusual symmetries of the system.
TL;DR: A new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems, which is dubbed as the neural stationary state ansatz, and shown to simulate various spin systems efficiently.
Abstract: A theoretical exploration of exotic properties in open quantum many-body systems requires an efficient search of the nonequillibrum stationary states. Aiming to accelerate the process, the authors develop here a variational method, in which the ansatz for the mixed states is based on the restricted Boltzmann machine, motivated by its high expressive power shown in various recent works. It is demonstrated that the ansatz successfully simulates dissipative spin systems both in one and two dimensions.
TL;DR: In this article, twisted bilayer grapheme was used to accommodate a plethora of interaction-driven quantum phases, since kinetic energy is quenched therein and electronic interactions therefore prevail.
Abstract: Flat electronic bands can accommodate a plethora of interaction-driven quantum phases, since kinetic energy is quenched therein and electronic interactions therefore prevail. Twisted bilayer graphe ...
TL;DR: In this paper, transfer matrices are used to explain the properties of non-Hermitian Hamiltonians and predict their topological properties, including their sensitivity to boundary conditions and a piling up of all states at the boundary, signalling a breakdown of the conventional bulk boundary correspondence.
Abstract: Non-Hermitian Hamiltonians---proposed to describe dissipative systems where the particles have a finite lifetime---exhibit many puzzling properties, strongly contrasting their Hermitian counterparts. In particular, their spectra exhibit extreme sensitivity to boundary conditions and a piling up of all states at the boundary, signalling a breakdown of the conventional bulk-boundary correspondence. The authors study these systems using transfer matrices, whereby they can explain as well as predict the aforementioned features without resorting to numerical computations. This analytical approach allows for a deeper understanding of the topological properties of non-Hermitian systems.
TL;DR: In this paper, the authors established an exact mapping between dynamical observables in random circuits and a statistical mechanical model of interacting spins, and used it to study systematically the entanglement generated by a random circuit consisting of local gates.
Abstract: Random unitary circuits are powerful minimal models for chaotic nonequilibrium evolution. Here, the authors establish an exact mapping between dynamical observables in random circuits and a statistical mechanical model of interacting spins, and use it to study systematically the entanglement generated by a random circuit consisting of local gates. A domain wall line tension in this spin model sets the entanglement growth rate. By a careful analysis of the interaction between domain walls, the authors derive explicitly the Kardar-Parisi-Zhang equation that governs the evolution of second Renyi entropy and identify a phase transition of the growth-rate function.